Aaron Swartz fought to "free" knowledge and information produced by (in many cases publicly funded) research that was and still is hoarded by the academic publishing industry so that they can profit of it.

What big AI companies have done is illegally hoovering up copyrighted creative output of individuals and creating a situation where the wages that normally would be paid to those individuals instead go to that one company (that stole their work) which now becomes disproportionally rich and powerful.

In both cases companies obtain money and power by hoarding information obtained through dubious means (in the former case most academics willingly participate while at the same tone they often don't really have a choice). Exactly what Swartz was fighting against.